Most uses of a d100 are for a DM
There are a lot of d100 random encounter tables on pages 92 - 112 in Xanathar’s Guide to Everything
There’s A framing event table in the DMG page 79, a dungeons location table page 99, there are d100 treasure tables pages 136 - 139; random magic item tables pages 144 - 149; several tables in the magic items section determining what the item’s effects are pages 135 - 213; tables for helping create sentient magic items pages 214 -217; tables for artefact properties pages 219 - 221; effects of madness pages 259 and 260; a number of tables on 293 - 301 for helping design dungeons
Page 140 of the DMG has a d100 table for a variant rule about mixing potions:
A character might drink one potion while still under the effects of another, or pour several potions into a single container. The strange ingredients used in creating potions can result in unpredictable interactions. When a character mixes two potions together, you can roll on the Potion Miscibility table. If more than two are combined, roll again for each subsequent potion, combining the results. Unless the effects are immediately obvious, reveal them only when they become evident.
The table details what might happen if you start mixing multiple potions together. Effects range from them blowing up in your face, turning to poison, working normally or becoming permanent. The most likely result though is that both potions simply work normally.
This spell instantly transports you [...] to a destination you select. [...] Your familiarily with the destinalion determines whelher you arrive there successfully. The DM rolls d100 and consults the table.
The DM rolls on the table for Teleportation whenever the spell is cast to determine if you arrive at your intended destination successfully. Different methods of using Teleportation or different levels of information determine which specific table you roll on as there are several tables in one block.
However, there are some for players
The carousing table in the DMG page 128 and the running a business table page 129 are meant to expand on the downtime activities options for players.
There are also a number of tables for player backstories in XGtE pages 61 - 73. There are also tables for character names pages 175 - 192.
The sorcerer’s wild magic table page 104 is an obvious one for players that springs to mind.
Trinket tables, PHB 160 and 161. They say that can also be used by the DM to help stock a dungeon.
Divine intervention, PHB page 59, requires a cleric to roll percentile dice (or a d100) to see if their god intervenes:
Imploring your deity's aid requires you to use your action. Describe the assistance you seek, and roll percentile dice. If you roll a number equal to or lower than your cleric level, your deity intervenes.
Allowing players to roll on DM tables
(Note that this section requires the DM to be willing to allow players to roll on DM tables. It is not guaranteed nor expected that your DM will allow for this, this is simply a suggestion which would allow for players to roll a d100 more frequently.)
User Phlarx pointed out that, although many tables are intended for use by the DM, a DM may allow the player to physically roll the d100 as the DM reads the result on the table. From their comment below this answer:
In our group, the DM has the players roll d100's for the treasure/item tables (he then looks up the results), going around the table until all treasure has then been accounted for. It has worked well for us, and I think it makes random loot a bit more engaging.
From user Phlarx’s experience, allowing players to roll on tables intended for the DM, such as the treasure and item tables, has increased player engagement in their game.
From this we may infer that allowing players to roll on other tables intended for DM use - such as the Teleportation table, the Mixing Potions table, or tables which determine what effect a magic item has - could also increase player engagement.
The process of allowing players to roll on DM tables may look like this, the appropriate dice being a d100 in the case of this question:
“The DM either picks a result from the table or determines if a roll is needed. If a roll is needed, the DM asks the player(s) involved to roll the appropriate dice. The DM reads the result of the roll and checks it against the table, reading out the result on the table.”